In 2006, when I was a depressed graduate student, I published an essay in n+1 magazine about the American short story. It was, I suggested, a dead form unnaturally perpetuated by fiction-writing workshops, after "the transcendental conditions for its existence" had, in the words of Lukács, "already been condemned by the historico-philosophical dialectic". Shortly after the essay was published, I received an email from a recent Columbia graduate called Ezra Koenig, to the effect that these words "really resonated" with him: would I mind sending him my address, so that he could mail me some short stories he had written in a creative-writing workshop?

What kind of person responds to an essay on the death of the short story by mailing its author some short stories? A very young person, clearly; this youthfulness was confirmed by the fact that the stories - for which, in all honesty, I did not have very high hopes - were accompanied by a self-produced CD of related songs performed by Koenig's band, Vampire Weekend.

In my experience, the problem of the undergraduate artist isn't technique so much as the mode of audience engagement, which tends towards either a kind of needy, insistent quality or its equally tiresome opposite: disaffected too-cool-for-schoolness. Then there is the propensity of youth to infuse its works with an atmosphere of melancholy or rage, which, when insufficiently explained, produces such a wearisome effect. These, at any rate, were some of the tendencies I was expecting - yet they were totally missing in either the stories or the CD.

The stories were stapled in a homemade booklet, entitled Cape Cod Kwassa Kwassa; the cover art was a photo collage of shirts and sweaters, clipped from a J Crew catalogue (Orange Coral, Tangerine Heather, Harbor). Enclosed with the sky-blue CD was a charming note, handwritten on a small square of lined paper that appeared to have been cut, thriftily, from a larger piece of lined paper. The animating voice of all of these materials had a kind of winning, unselfconscious directness, which was also my overwhelming impression when I eventually saw Vampire Weekend perform live. Not only had I never witnessed such an intensely likeable pop performance; I had never conceived of the possibility of such intense likability in a pop performance.

When Vampire Weekend signed with XL and became the next big thing, I was thrilled. For a depressed graduate student, it isn't every day that someone mails you some powerfully uplifting short stories and songs, then transforms overnight into a pop star.

In recent months, various critics have described a similar emotional trajectory regarding Vampire Weekend: initial mistrust, followed by bemused surrender. "By rights they should be incredibly annoying," the reviews begin, "and yet ..." In the Guardian, Alexis Petridis has expressed irritation at the premise of the single "Mansard Roof" (a "plonking lyrical reference to 17th-century French architect François Mansart"), and yet, as "the song skips along, deft and weirdly life-affirming", it is impossible to dislike. The "mix of Afro-pop and Irish folk" in "Bryn" ought to sound "like something grisly you'd hear by mistake while wandering Glastonbury's outlying fields" - but, in fact, the effect of the "weird, striking riff" is "unfathomably fantastic".

Deft, weird, unfathomable, fantastic: why does this music have the effect it does? This is the mystery of "charm" itself, or at least the charm of a certain kind of pop music. Etymologically and mythologically, charm is linked not only with singing, but with the ability to lull people into sleeplike trances. I experienced charm firsthand last October, when I commemorated the end of my postgraduate education with a low-budget vacation in Spain and was persuaded to spend one night in a third-class sleeper car on a train: a windowless cubicle with six bunks, stacked in two rows, like drawers in a morgue. My fellow travellers included a drunk guy and a tiny couple accompanied by a large collection of Spanish salamis. Lying in my morgue-like drawer, I had thoughts such as "I will never fall asleep" and "This is even worse than writing a dissertation".

But I turned on my MP3 player and Vampire Weekend's "Oxford Comma" came on, and within two or three minutes the train car felt . . . not comfortable, but like a legitimate, interesting part of a larger world. There we all were, stacked in our bunks: there was the friend who had convinced me to take this train, engrossed now by what appeared to be an attempt to build a pillow out of some shoes; there was the drunk guy, sleeping peacefully; there were the tiny man and the tiny woman, who were so tiny that it really didn't seem to bother them to share their bunks with those huge plaid vinyl tote bags, full of salchichon and redolent chorizo and maybe even, quién sabe, an entire hock of air-cured ham. Beyond the shuddering walls, something was rushing by, probably the Pyrenean lowlands. Gone was the most annoying part of travel discomfort: the thought that "it might have been otherwise". I listened to the whole album. After "The Kids Don't Stand a Chance", I fell asleep and woke up in Madrid.

It was during my research on the workings of charm and pop music that I stumbled on Internet Vibes (internetvibes.blogspot.com/), a blog that Ezra Koenig kept in 2005-6, with the goal of categorising as many "vibes" as possible. A "rain/grey/British vibe", for example, incorporates the walk from a Barbour store (to look at wellington boots) to the Whitney Museum (to look at "some avant-garde shorts by Robert Beavers"), as well as the TV adaptation of Brideshead Revisited, the Scottish electronic duo Boards of Canada, "late 90s Radiohead/global anxiety/airports" and New Jersey.

A "vibe" turns out to be something like "local colour", with a historical dimension. What gives a vibe "authenticity" is its ability to evoke - using a small number of disparate elements - a certain time, place and milieu; a certain nexus of historic, geographic and cultural forces. Authenticity is a subject frequently raised by critics of Vampire Weekend, and anticipated on Koenig's blog. "What is authentic for a guy like me?" he asks, referring to his east-coast Jewish intellectual background. "Growing up Jewish, you are presented with three images of your people: DESERT NOMADS BUILDING PYRAMIDS; EASTERN-EUROPEAN SHTETL-DWELLERS WITH BIG BEARDS; AMERICAN LIBERALS WHO EAT CHINESE FOOD ALL THE TIME. Now do you see where I'm coming from?"

You do, I think; and you see also why Koenig chose the word "vibe", with its connotation of music and overtones. It is easy to imagine those "three images" of Koenig's people as three sounds in a pop song, something like klezmer plus Aida plus Stan Getz. No other artistic medium can simultaneously convey so many different elements as music, with its harmonies and counterpoints and layering of beats; no other medium is so instantly suggestive of a vibe.

The project of collecting and categorising vibes transforms the world and its music into a marvellous conspiracy, a vast, incredibly complicated symphony, overheard in brief snatches. Consider the episode of Internet Vibes in which Koenig, attracted by the album's "dope cover featuring a Wolf, a Whale, an Eagle and a SWIRLY RAINBOW", purchases Paul Winter's 1978 album, Common Ground. Much of Winter's work turns out to consist of "duets" between animals and musical instruments. "An African Fish Eagle goes up against Paul McCandless's unstoppable bebop oboe"; another track pits the howls of a "genuine Timber Wolf" against the wail of Winter's soprano saxophone. (The timber wolf gets a writing credit.) For Koenig, Winter represents not just a lucky find, but a great coincidence, because the record was an "amalgamation of a lot of things" he happened to have been thinking of, at just that time ("conservation biology, New Age, smooth-ish jazz, WORLD . . .").

At the Salvation Army a few weeks later, Koenig discovers another Winter record, packaged with a giant map representing North America (aka "Turtle Island") as the nexus of a "mythical system of Animal communication": "the Narwhal Messenger in Nova Scotia tells the Humpback Whale by the Arctic Circle who tells the Baby Seal in Alaska, etc."

The last link in the chain comes when Koenig, bicycling down Amsterdam Avenue, hears some Brazilian percussion emanating from the cathedral of St John the Divine, where a large crowd of white-robed people have gathered, together with "a camel and some donkeys". Pausing to investigate, Koenig is astounded to hear a beautiful soprano saxophone, played by none other than Paul Winter, who is standing right there in the cathedral of St John the Divine, with two parakeets on his shoulder.

That's what charm can do: it can show us the world as a wonderland of hidden connections. Another of Koenig's hobbies is identifying similar photographic distortions, in otherwise unrelated pictures from Facebook - for example, he collects snapshots in which the "N" on someone's New Balance sneakers, caught by the flashbulb, radiates an otherworldly glow. "Looking at those pictures at the same time really gives me a strange feeling in my gut. Is this what The Da Vinci Code is about?"

In a way, yes; it's about how an eye or ear for detail can transform individual experiences into part of a bigger picture. But there are good and bad ways of going about it. Take the often invoked comparison of Vampire Weekend to the films of Wes Anderson. Nobody can say Anderson doesn't have a genius for vibes, for "local colour" and the big picture, for the gorgeous interplay of historical-cultural forces in certain locations in the Upper West Side, the bottom of the sea, rural India, and so on. But what makes many of Anderson's films so annoying is that those intricate, breathtaking vistas usually turn out to have nothing to do with the lives of the main characters. The lives of the more autobiographical white American characters are never really integrated with the lives of the gorgeous ambient foreigners or fish. Seu Jorge is there, wearing a fez-like ski cap and singing David Bowie covers in Portuguese; the corpse of a little drowned Indian boy is literally immolated before our eyes - and all for the mere purpose of amplifying the self-pity of some emotionally stunted American thirtysomethings, still vying for the approval of their ageing, equally egotistical parents. Really, the Freemasons might as well be there in wet suits, playing the harmonica.

Today I imagine the Wes Anderson of The Life Aquatic with Steve Zissou not unlike the monstrous nautical pin-striped apparition from Vampire Weekend's "The Kids Don't Stand a Chance": the one who enters the scene by a "devastating backstroke / all the way from France / With shiny shiny cufflinks, / His shirtsleeve to enhance." His MO: "ignoring all their history / denying them romance". And that is the great achievement of Vampire Weekend: they don't deny anybody their romance. The songs are so efficient, the "influences" so seamlessly fused, that you can't really say where personal experience ends and exoticism begins.

The key advantage of Vampire Weekend over Wes Anderson lies in the fact that they have found their perfect medium. Anderson has not yet managed to integrate his fabulous miniature worlds with the actual dramas of real life - a much harder thing to do in a two-hour narrative film than in a four-minute pop song. Indeed, judging from his very early short stories, linear narrative isn't Koenig's strong suit either; but he has already mastered a certain pop synchronicity. The title story in his college collection, Cape Cod Kwassa Kwassa, is about a girl spending her childhood summers with her mother, driving around Welfleet in a white Volvo with an anti-apartheid bumper sticker, listening to Paul Simon's Graceland. Like the Vampire Weekend song by the same title, Cape Cod Kwassa Kwassa is about a kind of Graceland "vibe". For the little girl in the story, Graceland is a "playland, another Candy Land"; and yet it is also "a decaying southern mansion with a 'jungle room' . . . the temple that fat Elvis built to die in"; and then, too, it is "the middle-aged musings of a divorced Paul Simon and the fading spirit of your mother's activism". Pop music is perhaps the unique medium for expressing the truth about Graceland: "It is all of these things at once."

Although no pop music can provide a really satisfying answer to the question "What am I doing here?", Vampire Weekend at its best can offer you a fantasy of total integration into a certain place and time in the world; it can transform your experience into a "vibe". There is something potentially sinister about this transformation; I suspect this is what the band's detractors are responding to, when they complain about elitism, exploitation, and so on. Well, that's the sinister side of the power of charm. ("Charm your way across the Khyber Pass," Vampire Weekend suggests, in the song "M79".) You can't predict it, or control it, but succumbing is a great pleasure.